Question: $f(x) = 4x^2-17x+3 $ What is the value of the discriminant of $f$ ?
Explanation: The ${\text{discriminant}}$ is a part of the quadratic formula. The sign of the discriminant tells us whether there are two roots, one root, or no roots. $\dfrac{-b\pm{\sqrt{\overbrace{{b^2-4ac}}^{\text{discriminant}}}}}{2a}$ Discriminant Roots Positive Two real roots Zero One repeated real root Negative No real root Let's find the discriminant of $f$ : $\begin{aligned} {b^2-4ac}&=(-17)^2-4\cdot4\cdot3 \\\\ &=289-48 \\\\ &={241} \end{aligned}$ So how many real number zeros does $f$ have? Since the discriminant is positive, $f$ has $2$ distinct real number zeros. In conclusion: The discriminant of $f$ is ${241}$. $f$ has $2$ distinct real number zeros.